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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.dfp;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.analysis.solvers.AllowedSolution;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.MathInternalError;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NoBracketingException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.util.Incrementor;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.26"></a>
<FONT color="green">027</FONT>    <a name="line.27"></a>
<FONT color="green">028</FONT>    /**<a name="line.28"></a>
<FONT color="green">029</FONT>     * This class implements a modification of the &lt;a<a name="line.29"></a>
<FONT color="green">030</FONT>     * href="http://mathworld.wolfram.com/BrentsMethod.html"&gt; Brent algorithm&lt;/a&gt;.<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * The changes with respect to the original Brent algorithm are:<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;ul&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     *   &lt;li&gt;the returned value is chosen in the current interval according<a name="line.34"></a>
<FONT color="green">035</FONT>     *   to user specified {@link AllowedSolution},&lt;/li&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     *   &lt;li&gt;the maximal order for the invert polynomial root search is<a name="line.36"></a>
<FONT color="green">037</FONT>     *   user-specified instead of being invert quadratic only&lt;/li&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     * &lt;/ul&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * &lt;/p&gt;<a name="line.39"></a>
<FONT color="green">040</FONT>     * The given interval must bracket the root.<a name="line.40"></a>
<FONT color="green">041</FONT>     *<a name="line.41"></a>
<FONT color="green">042</FONT>     * @version $Id: BracketingNthOrderBrentSolverDFP.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.42"></a>
<FONT color="green">043</FONT>     */<a name="line.43"></a>
<FONT color="green">044</FONT>    public class BracketingNthOrderBrentSolverDFP {<a name="line.44"></a>
<FONT color="green">045</FONT>    <a name="line.45"></a>
<FONT color="green">046</FONT>       /** Maximal aging triggering an attempt to balance the bracketing interval. */<a name="line.46"></a>
<FONT color="green">047</FONT>        private static final int MAXIMAL_AGING = 2;<a name="line.47"></a>
<FONT color="green">048</FONT>    <a name="line.48"></a>
<FONT color="green">049</FONT>        /** Maximal order. */<a name="line.49"></a>
<FONT color="green">050</FONT>        private final int maximalOrder;<a name="line.50"></a>
<FONT color="green">051</FONT>    <a name="line.51"></a>
<FONT color="green">052</FONT>        /** Function value accuracy. */<a name="line.52"></a>
<FONT color="green">053</FONT>        private final Dfp functionValueAccuracy;<a name="line.53"></a>
<FONT color="green">054</FONT>    <a name="line.54"></a>
<FONT color="green">055</FONT>        /** Absolute accuracy. */<a name="line.55"></a>
<FONT color="green">056</FONT>        private final Dfp absoluteAccuracy;<a name="line.56"></a>
<FONT color="green">057</FONT>    <a name="line.57"></a>
<FONT color="green">058</FONT>        /** Relative accuracy. */<a name="line.58"></a>
<FONT color="green">059</FONT>        private final Dfp relativeAccuracy;<a name="line.59"></a>
<FONT color="green">060</FONT>    <a name="line.60"></a>
<FONT color="green">061</FONT>        /** Evaluations counter. */<a name="line.61"></a>
<FONT color="green">062</FONT>        private final Incrementor evaluations = new Incrementor();<a name="line.62"></a>
<FONT color="green">063</FONT>    <a name="line.63"></a>
<FONT color="green">064</FONT>        /**<a name="line.64"></a>
<FONT color="green">065</FONT>         * Construct a solver.<a name="line.65"></a>
<FONT color="green">066</FONT>         *<a name="line.66"></a>
<FONT color="green">067</FONT>         * @param relativeAccuracy Relative accuracy.<a name="line.67"></a>
<FONT color="green">068</FONT>         * @param absoluteAccuracy Absolute accuracy.<a name="line.68"></a>
<FONT color="green">069</FONT>         * @param functionValueAccuracy Function value accuracy.<a name="line.69"></a>
<FONT color="green">070</FONT>         * @param maximalOrder maximal order.<a name="line.70"></a>
<FONT color="green">071</FONT>         * @exception NumberIsTooSmallException if maximal order is lower than 2<a name="line.71"></a>
<FONT color="green">072</FONT>         */<a name="line.72"></a>
<FONT color="green">073</FONT>        public BracketingNthOrderBrentSolverDFP(final Dfp relativeAccuracy,<a name="line.73"></a>
<FONT color="green">074</FONT>                                                final Dfp absoluteAccuracy,<a name="line.74"></a>
<FONT color="green">075</FONT>                                                final Dfp functionValueAccuracy,<a name="line.75"></a>
<FONT color="green">076</FONT>                                                final int maximalOrder)<a name="line.76"></a>
<FONT color="green">077</FONT>            throws NumberIsTooSmallException {<a name="line.77"></a>
<FONT color="green">078</FONT>            if (maximalOrder &lt; 2) {<a name="line.78"></a>
<FONT color="green">079</FONT>                throw new NumberIsTooSmallException(maximalOrder, 2, true);<a name="line.79"></a>
<FONT color="green">080</FONT>            }<a name="line.80"></a>
<FONT color="green">081</FONT>            this.maximalOrder = maximalOrder;<a name="line.81"></a>
<FONT color="green">082</FONT>            this.absoluteAccuracy = absoluteAccuracy;<a name="line.82"></a>
<FONT color="green">083</FONT>            this.relativeAccuracy = relativeAccuracy;<a name="line.83"></a>
<FONT color="green">084</FONT>            this.functionValueAccuracy = functionValueAccuracy;<a name="line.84"></a>
<FONT color="green">085</FONT>        }<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>        /** Get the maximal order.<a name="line.87"></a>
<FONT color="green">088</FONT>         * @return maximal order<a name="line.88"></a>
<FONT color="green">089</FONT>         */<a name="line.89"></a>
<FONT color="green">090</FONT>        public int getMaximalOrder() {<a name="line.90"></a>
<FONT color="green">091</FONT>            return maximalOrder;<a name="line.91"></a>
<FONT color="green">092</FONT>        }<a name="line.92"></a>
<FONT color="green">093</FONT>    <a name="line.93"></a>
<FONT color="green">094</FONT>        /**<a name="line.94"></a>
<FONT color="green">095</FONT>         * Get the maximal number of function evaluations.<a name="line.95"></a>
<FONT color="green">096</FONT>         *<a name="line.96"></a>
<FONT color="green">097</FONT>         * @return the maximal number of function evaluations.<a name="line.97"></a>
<FONT color="green">098</FONT>         */<a name="line.98"></a>
<FONT color="green">099</FONT>        public int getMaxEvaluations() {<a name="line.99"></a>
<FONT color="green">100</FONT>            return evaluations.getMaximalCount();<a name="line.100"></a>
<FONT color="green">101</FONT>        }<a name="line.101"></a>
<FONT color="green">102</FONT>    <a name="line.102"></a>
<FONT color="green">103</FONT>        /**<a name="line.103"></a>
<FONT color="green">104</FONT>         * Get the number of evaluations of the objective function.<a name="line.104"></a>
<FONT color="green">105</FONT>         * The number of evaluations corresponds to the last call to the<a name="line.105"></a>
<FONT color="green">106</FONT>         * {@code optimize} method. It is 0 if the method has not been<a name="line.106"></a>
<FONT color="green">107</FONT>         * called yet.<a name="line.107"></a>
<FONT color="green">108</FONT>         *<a name="line.108"></a>
<FONT color="green">109</FONT>         * @return the number of evaluations of the objective function.<a name="line.109"></a>
<FONT color="green">110</FONT>         */<a name="line.110"></a>
<FONT color="green">111</FONT>        public int getEvaluations() {<a name="line.111"></a>
<FONT color="green">112</FONT>            return evaluations.getCount();<a name="line.112"></a>
<FONT color="green">113</FONT>        }<a name="line.113"></a>
<FONT color="green">114</FONT>    <a name="line.114"></a>
<FONT color="green">115</FONT>        /**<a name="line.115"></a>
<FONT color="green">116</FONT>         * Get the absolute accuracy.<a name="line.116"></a>
<FONT color="green">117</FONT>         * @return absolute accuracy<a name="line.117"></a>
<FONT color="green">118</FONT>         */<a name="line.118"></a>
<FONT color="green">119</FONT>        public Dfp getAbsoluteAccuracy() {<a name="line.119"></a>
<FONT color="green">120</FONT>            return absoluteAccuracy;<a name="line.120"></a>
<FONT color="green">121</FONT>        }<a name="line.121"></a>
<FONT color="green">122</FONT>    <a name="line.122"></a>
<FONT color="green">123</FONT>        /**<a name="line.123"></a>
<FONT color="green">124</FONT>         * Get the relative accuracy.<a name="line.124"></a>
<FONT color="green">125</FONT>         * @return relative accuracy<a name="line.125"></a>
<FONT color="green">126</FONT>         */<a name="line.126"></a>
<FONT color="green">127</FONT>        public Dfp getRelativeAccuracy() {<a name="line.127"></a>
<FONT color="green">128</FONT>            return relativeAccuracy;<a name="line.128"></a>
<FONT color="green">129</FONT>        }<a name="line.129"></a>
<FONT color="green">130</FONT>    <a name="line.130"></a>
<FONT color="green">131</FONT>        /**<a name="line.131"></a>
<FONT color="green">132</FONT>         * Get the function accuracy.<a name="line.132"></a>
<FONT color="green">133</FONT>         * @return function accuracy<a name="line.133"></a>
<FONT color="green">134</FONT>         */<a name="line.134"></a>
<FONT color="green">135</FONT>        public Dfp getFunctionValueAccuracy() {<a name="line.135"></a>
<FONT color="green">136</FONT>            return functionValueAccuracy;<a name="line.136"></a>
<FONT color="green">137</FONT>        }<a name="line.137"></a>
<FONT color="green">138</FONT>    <a name="line.138"></a>
<FONT color="green">139</FONT>        /**<a name="line.139"></a>
<FONT color="green">140</FONT>         * Solve for a zero in the given interval.<a name="line.140"></a>
<FONT color="green">141</FONT>         * A solver may require that the interval brackets a single zero root.<a name="line.141"></a>
<FONT color="green">142</FONT>         * Solvers that do require bracketing should be able to handle the case<a name="line.142"></a>
<FONT color="green">143</FONT>         * where one of the endpoints is itself a root.<a name="line.143"></a>
<FONT color="green">144</FONT>         *<a name="line.144"></a>
<FONT color="green">145</FONT>         * @param maxEval Maximum number of evaluations.<a name="line.145"></a>
<FONT color="green">146</FONT>         * @param f Function to solve.<a name="line.146"></a>
<FONT color="green">147</FONT>         * @param min Lower bound for the interval.<a name="line.147"></a>
<FONT color="green">148</FONT>         * @param max Upper bound for the interval.<a name="line.148"></a>
<FONT color="green">149</FONT>         * @param allowedSolution The kind of solutions that the root-finding algorithm may<a name="line.149"></a>
<FONT color="green">150</FONT>         * accept as solutions.<a name="line.150"></a>
<FONT color="green">151</FONT>         * @return a value where the function is zero.<a name="line.151"></a>
<FONT color="green">152</FONT>         * @exception NullArgumentException if f is null.<a name="line.152"></a>
<FONT color="green">153</FONT>         * @exception NoBracketingException if root cannot be bracketed<a name="line.153"></a>
<FONT color="green">154</FONT>         */<a name="line.154"></a>
<FONT color="green">155</FONT>        public Dfp solve(final int maxEval, final UnivariateDfpFunction f,<a name="line.155"></a>
<FONT color="green">156</FONT>                         final Dfp min, final Dfp max, final AllowedSolution allowedSolution)<a name="line.156"></a>
<FONT color="green">157</FONT>            throws NullArgumentException, NoBracketingException {<a name="line.157"></a>
<FONT color="green">158</FONT>            return solve(maxEval, f, min, max, min.add(max).divide(2), allowedSolution);<a name="line.158"></a>
<FONT color="green">159</FONT>        }<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>        /**<a name="line.161"></a>
<FONT color="green">162</FONT>         * Solve for a zero in the given interval, start at {@code startValue}.<a name="line.162"></a>
<FONT color="green">163</FONT>         * A solver may require that the interval brackets a single zero root.<a name="line.163"></a>
<FONT color="green">164</FONT>         * Solvers that do require bracketing should be able to handle the case<a name="line.164"></a>
<FONT color="green">165</FONT>         * where one of the endpoints is itself a root.<a name="line.165"></a>
<FONT color="green">166</FONT>         *<a name="line.166"></a>
<FONT color="green">167</FONT>         * @param maxEval Maximum number of evaluations.<a name="line.167"></a>
<FONT color="green">168</FONT>         * @param f Function to solve.<a name="line.168"></a>
<FONT color="green">169</FONT>         * @param min Lower bound for the interval.<a name="line.169"></a>
<FONT color="green">170</FONT>         * @param max Upper bound for the interval.<a name="line.170"></a>
<FONT color="green">171</FONT>         * @param startValue Start value to use.<a name="line.171"></a>
<FONT color="green">172</FONT>         * @param allowedSolution The kind of solutions that the root-finding algorithm may<a name="line.172"></a>
<FONT color="green">173</FONT>         * accept as solutions.<a name="line.173"></a>
<FONT color="green">174</FONT>         * @return a value where the function is zero.<a name="line.174"></a>
<FONT color="green">175</FONT>         * @exception NullArgumentException if f is null.<a name="line.175"></a>
<FONT color="green">176</FONT>         * @exception NoBracketingException if root cannot be bracketed<a name="line.176"></a>
<FONT color="green">177</FONT>         */<a name="line.177"></a>
<FONT color="green">178</FONT>        public Dfp solve(final int maxEval, final UnivariateDfpFunction f,<a name="line.178"></a>
<FONT color="green">179</FONT>                         final Dfp min, final Dfp max, final Dfp startValue,<a name="line.179"></a>
<FONT color="green">180</FONT>                         final AllowedSolution allowedSolution)<a name="line.180"></a>
<FONT color="green">181</FONT>            throws NullArgumentException, NoBracketingException {<a name="line.181"></a>
<FONT color="green">182</FONT>    <a name="line.182"></a>
<FONT color="green">183</FONT>            // Checks.<a name="line.183"></a>
<FONT color="green">184</FONT>            MathUtils.checkNotNull(f);<a name="line.184"></a>
<FONT color="green">185</FONT>    <a name="line.185"></a>
<FONT color="green">186</FONT>            // Reset.<a name="line.186"></a>
<FONT color="green">187</FONT>            evaluations.setMaximalCount(maxEval);<a name="line.187"></a>
<FONT color="green">188</FONT>            evaluations.resetCount();<a name="line.188"></a>
<FONT color="green">189</FONT>            Dfp zero = startValue.getZero();<a name="line.189"></a>
<FONT color="green">190</FONT>            Dfp nan  = zero.newInstance((byte) 1, Dfp.QNAN);<a name="line.190"></a>
<FONT color="green">191</FONT>    <a name="line.191"></a>
<FONT color="green">192</FONT>            // prepare arrays with the first points<a name="line.192"></a>
<FONT color="green">193</FONT>            final Dfp[] x = new Dfp[maximalOrder + 1];<a name="line.193"></a>
<FONT color="green">194</FONT>            final Dfp[] y = new Dfp[maximalOrder + 1];<a name="line.194"></a>
<FONT color="green">195</FONT>            x[0] = min;<a name="line.195"></a>
<FONT color="green">196</FONT>            x[1] = startValue;<a name="line.196"></a>
<FONT color="green">197</FONT>            x[2] = max;<a name="line.197"></a>
<FONT color="green">198</FONT>    <a name="line.198"></a>
<FONT color="green">199</FONT>            // evaluate initial guess<a name="line.199"></a>
<FONT color="green">200</FONT>            evaluations.incrementCount();<a name="line.200"></a>
<FONT color="green">201</FONT>            y[1] = f.value(x[1]);<a name="line.201"></a>
<FONT color="green">202</FONT>            if (y[1].isZero()) {<a name="line.202"></a>
<FONT color="green">203</FONT>                // return the initial guess if it is a perfect root.<a name="line.203"></a>
<FONT color="green">204</FONT>                return x[1];<a name="line.204"></a>
<FONT color="green">205</FONT>            }<a name="line.205"></a>
<FONT color="green">206</FONT>    <a name="line.206"></a>
<FONT color="green">207</FONT>            // evaluate first  endpoint<a name="line.207"></a>
<FONT color="green">208</FONT>            evaluations.incrementCount();<a name="line.208"></a>
<FONT color="green">209</FONT>            y[0] = f.value(x[0]);<a name="line.209"></a>
<FONT color="green">210</FONT>            if (y[0].isZero()) {<a name="line.210"></a>
<FONT color="green">211</FONT>                // return the first endpoint if it is a perfect root.<a name="line.211"></a>
<FONT color="green">212</FONT>                return x[0];<a name="line.212"></a>
<FONT color="green">213</FONT>            }<a name="line.213"></a>
<FONT color="green">214</FONT>    <a name="line.214"></a>
<FONT color="green">215</FONT>            int nbPoints;<a name="line.215"></a>
<FONT color="green">216</FONT>            int signChangeIndex;<a name="line.216"></a>
<FONT color="green">217</FONT>            if (y[0].multiply(y[1]).negativeOrNull()) {<a name="line.217"></a>
<FONT color="green">218</FONT>    <a name="line.218"></a>
<FONT color="green">219</FONT>                // reduce interval if it brackets the root<a name="line.219"></a>
<FONT color="green">220</FONT>                nbPoints        = 2;<a name="line.220"></a>
<FONT color="green">221</FONT>                signChangeIndex = 1;<a name="line.221"></a>
<FONT color="green">222</FONT>    <a name="line.222"></a>
<FONT color="green">223</FONT>            } else {<a name="line.223"></a>
<FONT color="green">224</FONT>    <a name="line.224"></a>
<FONT color="green">225</FONT>                // evaluate second endpoint<a name="line.225"></a>
<FONT color="green">226</FONT>                evaluations.incrementCount();<a name="line.226"></a>
<FONT color="green">227</FONT>                y[2] = f.value(x[2]);<a name="line.227"></a>
<FONT color="green">228</FONT>                if (y[2].isZero()) {<a name="line.228"></a>
<FONT color="green">229</FONT>                    // return the second endpoint if it is a perfect root.<a name="line.229"></a>
<FONT color="green">230</FONT>                    return x[2];<a name="line.230"></a>
<FONT color="green">231</FONT>                }<a name="line.231"></a>
<FONT color="green">232</FONT>    <a name="line.232"></a>
<FONT color="green">233</FONT>                if (y[1].multiply(y[2]).negativeOrNull()) {<a name="line.233"></a>
<FONT color="green">234</FONT>                    // use all computed point as a start sampling array for solving<a name="line.234"></a>
<FONT color="green">235</FONT>                    nbPoints        = 3;<a name="line.235"></a>
<FONT color="green">236</FONT>                    signChangeIndex = 2;<a name="line.236"></a>
<FONT color="green">237</FONT>                } else {<a name="line.237"></a>
<FONT color="green">238</FONT>                    throw new NoBracketingException(x[0].toDouble(), x[2].toDouble(),<a name="line.238"></a>
<FONT color="green">239</FONT>                                                    y[0].toDouble(), y[2].toDouble());<a name="line.239"></a>
<FONT color="green">240</FONT>                }<a name="line.240"></a>
<FONT color="green">241</FONT>    <a name="line.241"></a>
<FONT color="green">242</FONT>            }<a name="line.242"></a>
<FONT color="green">243</FONT>    <a name="line.243"></a>
<FONT color="green">244</FONT>            // prepare a work array for inverse polynomial interpolation<a name="line.244"></a>
<FONT color="green">245</FONT>            final Dfp[] tmpX = new Dfp[x.length];<a name="line.245"></a>
<FONT color="green">246</FONT>    <a name="line.246"></a>
<FONT color="green">247</FONT>            // current tightest bracketing of the root<a name="line.247"></a>
<FONT color="green">248</FONT>            Dfp xA    = x[signChangeIndex - 1];<a name="line.248"></a>
<FONT color="green">249</FONT>            Dfp yA    = y[signChangeIndex - 1];<a name="line.249"></a>
<FONT color="green">250</FONT>            Dfp absXA = xA.abs();<a name="line.250"></a>
<FONT color="green">251</FONT>            Dfp absYA = yA.abs();<a name="line.251"></a>
<FONT color="green">252</FONT>            int agingA   = 0;<a name="line.252"></a>
<FONT color="green">253</FONT>            Dfp xB    = x[signChangeIndex];<a name="line.253"></a>
<FONT color="green">254</FONT>            Dfp yB    = y[signChangeIndex];<a name="line.254"></a>
<FONT color="green">255</FONT>            Dfp absXB = xB.abs();<a name="line.255"></a>
<FONT color="green">256</FONT>            Dfp absYB = yB.abs();<a name="line.256"></a>
<FONT color="green">257</FONT>            int agingB   = 0;<a name="line.257"></a>
<FONT color="green">258</FONT>    <a name="line.258"></a>
<FONT color="green">259</FONT>            // search loop<a name="line.259"></a>
<FONT color="green">260</FONT>            while (true) {<a name="line.260"></a>
<FONT color="green">261</FONT>    <a name="line.261"></a>
<FONT color="green">262</FONT>                // check convergence of bracketing interval<a name="line.262"></a>
<FONT color="green">263</FONT>                Dfp maxX = absXA.lessThan(absXB) ? absXB : absXA;<a name="line.263"></a>
<FONT color="green">264</FONT>                Dfp maxY = absYA.lessThan(absYB) ? absYB : absYA;<a name="line.264"></a>
<FONT color="green">265</FONT>                final Dfp xTol = absoluteAccuracy.add(relativeAccuracy.multiply(maxX));<a name="line.265"></a>
<FONT color="green">266</FONT>                if (xB.subtract(xA).subtract(xTol).negativeOrNull() ||<a name="line.266"></a>
<FONT color="green">267</FONT>                    maxY.lessThan(functionValueAccuracy)) {<a name="line.267"></a>
<FONT color="green">268</FONT>                    switch (allowedSolution) {<a name="line.268"></a>
<FONT color="green">269</FONT>                    case ANY_SIDE :<a name="line.269"></a>
<FONT color="green">270</FONT>                        return absYA.lessThan(absYB) ? xA : xB;<a name="line.270"></a>
<FONT color="green">271</FONT>                    case LEFT_SIDE :<a name="line.271"></a>
<FONT color="green">272</FONT>                        return xA;<a name="line.272"></a>
<FONT color="green">273</FONT>                    case RIGHT_SIDE :<a name="line.273"></a>
<FONT color="green">274</FONT>                        return xB;<a name="line.274"></a>
<FONT color="green">275</FONT>                    case BELOW_SIDE :<a name="line.275"></a>
<FONT color="green">276</FONT>                        return yA.lessThan(zero) ? xA : xB;<a name="line.276"></a>
<FONT color="green">277</FONT>                    case ABOVE_SIDE :<a name="line.277"></a>
<FONT color="green">278</FONT>                        return yA.lessThan(zero) ? xB : xA;<a name="line.278"></a>
<FONT color="green">279</FONT>                    default :<a name="line.279"></a>
<FONT color="green">280</FONT>                        // this should never happen<a name="line.280"></a>
<FONT color="green">281</FONT>                        throw new MathInternalError(null);<a name="line.281"></a>
<FONT color="green">282</FONT>                    }<a name="line.282"></a>
<FONT color="green">283</FONT>                }<a name="line.283"></a>
<FONT color="green">284</FONT>    <a name="line.284"></a>
<FONT color="green">285</FONT>                // target for the next evaluation point<a name="line.285"></a>
<FONT color="green">286</FONT>                Dfp targetY;<a name="line.286"></a>
<FONT color="green">287</FONT>                if (agingA &gt;= MAXIMAL_AGING) {<a name="line.287"></a>
<FONT color="green">288</FONT>                    // we keep updating the high bracket, try to compensate this<a name="line.288"></a>
<FONT color="green">289</FONT>                    targetY = yB.divide(16).negate();<a name="line.289"></a>
<FONT color="green">290</FONT>                } else if (agingB &gt;= MAXIMAL_AGING) {<a name="line.290"></a>
<FONT color="green">291</FONT>                    // we keep updating the low bracket, try to compensate this<a name="line.291"></a>
<FONT color="green">292</FONT>                    targetY = yA.divide(16).negate();<a name="line.292"></a>
<FONT color="green">293</FONT>                } else {<a name="line.293"></a>
<FONT color="green">294</FONT>                    // bracketing is balanced, try to find the root itself<a name="line.294"></a>
<FONT color="green">295</FONT>                    targetY = zero;<a name="line.295"></a>
<FONT color="green">296</FONT>                }<a name="line.296"></a>
<FONT color="green">297</FONT>    <a name="line.297"></a>
<FONT color="green">298</FONT>                // make a few attempts to guess a root,<a name="line.298"></a>
<FONT color="green">299</FONT>                Dfp nextX;<a name="line.299"></a>
<FONT color="green">300</FONT>                int start = 0;<a name="line.300"></a>
<FONT color="green">301</FONT>                int end   = nbPoints;<a name="line.301"></a>
<FONT color="green">302</FONT>                do {<a name="line.302"></a>
<FONT color="green">303</FONT>    <a name="line.303"></a>
<FONT color="green">304</FONT>                    // guess a value for current target, using inverse polynomial interpolation<a name="line.304"></a>
<FONT color="green">305</FONT>                    System.arraycopy(x, start, tmpX, start, end - start);<a name="line.305"></a>
<FONT color="green">306</FONT>                    nextX = guessX(targetY, tmpX, y, start, end);<a name="line.306"></a>
<FONT color="green">307</FONT>    <a name="line.307"></a>
<FONT color="green">308</FONT>                    if (!(nextX.greaterThan(xA) &amp;&amp; nextX.lessThan(xB))) {<a name="line.308"></a>
<FONT color="green">309</FONT>                        // the guessed root is not strictly inside of the tightest bracketing interval<a name="line.309"></a>
<FONT color="green">310</FONT>    <a name="line.310"></a>
<FONT color="green">311</FONT>                        // the guessed root is either not strictly inside the interval or it<a name="line.311"></a>
<FONT color="green">312</FONT>                        // is a NaN (which occurs when some sampling points share the same y)<a name="line.312"></a>
<FONT color="green">313</FONT>                        // we try again with a lower interpolation order<a name="line.313"></a>
<FONT color="green">314</FONT>                        if (signChangeIndex - start &gt;= end - signChangeIndex) {<a name="line.314"></a>
<FONT color="green">315</FONT>                            // we have more points before the sign change, drop the lowest point<a name="line.315"></a>
<FONT color="green">316</FONT>                            ++start;<a name="line.316"></a>
<FONT color="green">317</FONT>                        } else {<a name="line.317"></a>
<FONT color="green">318</FONT>                            // we have more points after sign change, drop the highest point<a name="line.318"></a>
<FONT color="green">319</FONT>                            --end;<a name="line.319"></a>
<FONT color="green">320</FONT>                        }<a name="line.320"></a>
<FONT color="green">321</FONT>    <a name="line.321"></a>
<FONT color="green">322</FONT>                        // we need to do one more attempt<a name="line.322"></a>
<FONT color="green">323</FONT>                        nextX = nan;<a name="line.323"></a>
<FONT color="green">324</FONT>    <a name="line.324"></a>
<FONT color="green">325</FONT>                    }<a name="line.325"></a>
<FONT color="green">326</FONT>    <a name="line.326"></a>
<FONT color="green">327</FONT>                } while (nextX.isNaN() &amp;&amp; (end - start &gt; 1));<a name="line.327"></a>
<FONT color="green">328</FONT>    <a name="line.328"></a>
<FONT color="green">329</FONT>                if (nextX.isNaN()) {<a name="line.329"></a>
<FONT color="green">330</FONT>                    // fall back to bisection<a name="line.330"></a>
<FONT color="green">331</FONT>                    nextX = xA.add(xB.subtract(xA).divide(2));<a name="line.331"></a>
<FONT color="green">332</FONT>                    start = signChangeIndex - 1;<a name="line.332"></a>
<FONT color="green">333</FONT>                    end   = signChangeIndex;<a name="line.333"></a>
<FONT color="green">334</FONT>                }<a name="line.334"></a>
<FONT color="green">335</FONT>    <a name="line.335"></a>
<FONT color="green">336</FONT>                // evaluate the function at the guessed root<a name="line.336"></a>
<FONT color="green">337</FONT>                evaluations.incrementCount();<a name="line.337"></a>
<FONT color="green">338</FONT>                final Dfp nextY = f.value(nextX);<a name="line.338"></a>
<FONT color="green">339</FONT>                if (nextY.isZero()) {<a name="line.339"></a>
<FONT color="green">340</FONT>                    // we have found an exact root, since it is not an approximation<a name="line.340"></a>
<FONT color="green">341</FONT>                    // we don't need to bother about the allowed solutions setting<a name="line.341"></a>
<FONT color="green">342</FONT>                    return nextX;<a name="line.342"></a>
<FONT color="green">343</FONT>                }<a name="line.343"></a>
<FONT color="green">344</FONT>    <a name="line.344"></a>
<FONT color="green">345</FONT>                if ((nbPoints &gt; 2) &amp;&amp; (end - start != nbPoints)) {<a name="line.345"></a>
<FONT color="green">346</FONT>    <a name="line.346"></a>
<FONT color="green">347</FONT>                    // we have been forced to ignore some points to keep bracketing,<a name="line.347"></a>
<FONT color="green">348</FONT>                    // they are probably too far from the root, drop them from now on<a name="line.348"></a>
<FONT color="green">349</FONT>                    nbPoints = end - start;<a name="line.349"></a>
<FONT color="green">350</FONT>                    System.arraycopy(x, start, x, 0, nbPoints);<a name="line.350"></a>
<FONT color="green">351</FONT>                    System.arraycopy(y, start, y, 0, nbPoints);<a name="line.351"></a>
<FONT color="green">352</FONT>                    signChangeIndex -= start;<a name="line.352"></a>
<FONT color="green">353</FONT>    <a name="line.353"></a>
<FONT color="green">354</FONT>                } else  if (nbPoints == x.length) {<a name="line.354"></a>
<FONT color="green">355</FONT>    <a name="line.355"></a>
<FONT color="green">356</FONT>                    // we have to drop one point in order to insert the new one<a name="line.356"></a>
<FONT color="green">357</FONT>                    nbPoints--;<a name="line.357"></a>
<FONT color="green">358</FONT>    <a name="line.358"></a>
<FONT color="green">359</FONT>                    // keep the tightest bracketing interval as centered as possible<a name="line.359"></a>
<FONT color="green">360</FONT>                    if (signChangeIndex &gt;= (x.length + 1) / 2) {<a name="line.360"></a>
<FONT color="green">361</FONT>                        // we drop the lowest point, we have to shift the arrays and the index<a name="line.361"></a>
<FONT color="green">362</FONT>                        System.arraycopy(x, 1, x, 0, nbPoints);<a name="line.362"></a>
<FONT color="green">363</FONT>                        System.arraycopy(y, 1, y, 0, nbPoints);<a name="line.363"></a>
<FONT color="green">364</FONT>                        --signChangeIndex;<a name="line.364"></a>
<FONT color="green">365</FONT>                    }<a name="line.365"></a>
<FONT color="green">366</FONT>    <a name="line.366"></a>
<FONT color="green">367</FONT>                }<a name="line.367"></a>
<FONT color="green">368</FONT>    <a name="line.368"></a>
<FONT color="green">369</FONT>                // insert the last computed point<a name="line.369"></a>
<FONT color="green">370</FONT>                //(by construction, we know it lies inside the tightest bracketing interval)<a name="line.370"></a>
<FONT color="green">371</FONT>                System.arraycopy(x, signChangeIndex, x, signChangeIndex + 1, nbPoints - signChangeIndex);<a name="line.371"></a>
<FONT color="green">372</FONT>                x[signChangeIndex] = nextX;<a name="line.372"></a>
<FONT color="green">373</FONT>                System.arraycopy(y, signChangeIndex, y, signChangeIndex + 1, nbPoints - signChangeIndex);<a name="line.373"></a>
<FONT color="green">374</FONT>                y[signChangeIndex] = nextY;<a name="line.374"></a>
<FONT color="green">375</FONT>                ++nbPoints;<a name="line.375"></a>
<FONT color="green">376</FONT>    <a name="line.376"></a>
<FONT color="green">377</FONT>                // update the bracketing interval<a name="line.377"></a>
<FONT color="green">378</FONT>                if (nextY.multiply(yA).negativeOrNull()) {<a name="line.378"></a>
<FONT color="green">379</FONT>                    // the sign change occurs before the inserted point<a name="line.379"></a>
<FONT color="green">380</FONT>                    xB = nextX;<a name="line.380"></a>
<FONT color="green">381</FONT>                    yB = nextY;<a name="line.381"></a>
<FONT color="green">382</FONT>                    absYB = yB.abs();<a name="line.382"></a>
<FONT color="green">383</FONT>                    ++agingA;<a name="line.383"></a>
<FONT color="green">384</FONT>                    agingB = 0;<a name="line.384"></a>
<FONT color="green">385</FONT>                } else {<a name="line.385"></a>
<FONT color="green">386</FONT>                    // the sign change occurs after the inserted point<a name="line.386"></a>
<FONT color="green">387</FONT>                    xA = nextX;<a name="line.387"></a>
<FONT color="green">388</FONT>                    yA = nextY;<a name="line.388"></a>
<FONT color="green">389</FONT>                    absYA = yA.abs();<a name="line.389"></a>
<FONT color="green">390</FONT>                    agingA = 0;<a name="line.390"></a>
<FONT color="green">391</FONT>                    ++agingB;<a name="line.391"></a>
<FONT color="green">392</FONT>    <a name="line.392"></a>
<FONT color="green">393</FONT>                    // update the sign change index<a name="line.393"></a>
<FONT color="green">394</FONT>                    signChangeIndex++;<a name="line.394"></a>
<FONT color="green">395</FONT>    <a name="line.395"></a>
<FONT color="green">396</FONT>                }<a name="line.396"></a>
<FONT color="green">397</FONT>    <a name="line.397"></a>
<FONT color="green">398</FONT>            }<a name="line.398"></a>
<FONT color="green">399</FONT>    <a name="line.399"></a>
<FONT color="green">400</FONT>        }<a name="line.400"></a>
<FONT color="green">401</FONT>    <a name="line.401"></a>
<FONT color="green">402</FONT>        /** Guess an x value by n&lt;sup&gt;th&lt;/sup&gt; order inverse polynomial interpolation.<a name="line.402"></a>
<FONT color="green">403</FONT>         * &lt;p&gt;<a name="line.403"></a>
<FONT color="green">404</FONT>         * The x value is guessed by evaluating polynomial Q(y) at y = targetY, where Q<a name="line.404"></a>
<FONT color="green">405</FONT>         * is built such that for all considered points (x&lt;sub&gt;i&lt;/sub&gt;, y&lt;sub&gt;i&lt;/sub&gt;),<a name="line.405"></a>
<FONT color="green">406</FONT>         * Q(y&lt;sub&gt;i&lt;/sub&gt;) = x&lt;sub&gt;i&lt;/sub&gt;.<a name="line.406"></a>
<FONT color="green">407</FONT>         * &lt;/p&gt;<a name="line.407"></a>
<FONT color="green">408</FONT>         * @param targetY target value for y<a name="line.408"></a>
<FONT color="green">409</FONT>         * @param x reference points abscissas for interpolation,<a name="line.409"></a>
<FONT color="green">410</FONT>         * note that this array &lt;em&gt;is&lt;/em&gt; modified during computation<a name="line.410"></a>
<FONT color="green">411</FONT>         * @param y reference points ordinates for interpolation<a name="line.411"></a>
<FONT color="green">412</FONT>         * @param start start index of the points to consider (inclusive)<a name="line.412"></a>
<FONT color="green">413</FONT>         * @param end end index of the points to consider (exclusive)<a name="line.413"></a>
<FONT color="green">414</FONT>         * @return guessed root (will be a NaN if two points share the same y)<a name="line.414"></a>
<FONT color="green">415</FONT>         */<a name="line.415"></a>
<FONT color="green">416</FONT>        private Dfp guessX(final Dfp targetY, final Dfp[] x, final Dfp[] y,<a name="line.416"></a>
<FONT color="green">417</FONT>                           final int start, final int end) {<a name="line.417"></a>
<FONT color="green">418</FONT>    <a name="line.418"></a>
<FONT color="green">419</FONT>            // compute Q Newton coefficients by divided differences<a name="line.419"></a>
<FONT color="green">420</FONT>            for (int i = start; i &lt; end - 1; ++i) {<a name="line.420"></a>
<FONT color="green">421</FONT>                final int delta = i + 1 - start;<a name="line.421"></a>
<FONT color="green">422</FONT>                for (int j = end - 1; j &gt; i; --j) {<a name="line.422"></a>
<FONT color="green">423</FONT>                    x[j] = x[j].subtract(x[j-1]).divide(y[j].subtract(y[j - delta]));<a name="line.423"></a>
<FONT color="green">424</FONT>                }<a name="line.424"></a>
<FONT color="green">425</FONT>            }<a name="line.425"></a>
<FONT color="green">426</FONT>    <a name="line.426"></a>
<FONT color="green">427</FONT>            // evaluate Q(targetY)<a name="line.427"></a>
<FONT color="green">428</FONT>            Dfp x0 = targetY.getZero();<a name="line.428"></a>
<FONT color="green">429</FONT>            for (int j = end - 1; j &gt;= start; --j) {<a name="line.429"></a>
<FONT color="green">430</FONT>                x0 = x[j].add(x0.multiply(targetY.subtract(y[j])));<a name="line.430"></a>
<FONT color="green">431</FONT>            }<a name="line.431"></a>
<FONT color="green">432</FONT>    <a name="line.432"></a>
<FONT color="green">433</FONT>            return x0;<a name="line.433"></a>
<FONT color="green">434</FONT>    <a name="line.434"></a>
<FONT color="green">435</FONT>        }<a name="line.435"></a>
<FONT color="green">436</FONT>    <a name="line.436"></a>
<FONT color="green">437</FONT>    }<a name="line.437"></a>




























































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